Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing

This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function , . The global existence of the unique boun...

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Published inNonlinearity Vol. 32; no. 4; pp. 1327 - 1351
Main Authors Ahn, Jaewook, Yoon, Changwook
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.04.2019
Subjects
chemotaxis
global existence
Lyapunov functional
motility function
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Abstract This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function , . The global existence of the unique bounded classical solutions is established without smallness of the initial data neither the convexity of the domain when , or , . In addition, we find the conditions on parameters, and , that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.
AbstractList This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux boundary conditions. The system contains a Fokker-Planck type diffusion with a motility function , . The global existence of the unique bounded classical solutions is established without smallness of the initial data neither the convexity of the domain when , or , . In addition, we find the conditions on parameters, and , that make the spatially homogeneous equilibrium solution globally stable or linearly unstable.
Author Yoon, Changwook
Ahn, Jaewook
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Cites_doi 10.1090/mmono/114
10.3934/dcdsb.2016.21.81
10.1002/mma.3489
10.1080/03605307908820113
10.1016/j.na.2018.01.002
10.1103/PhysRevLett.108.198102
10.1002/cpa.3160440705
10.1006/jdeq.1993.1045
10.1016/0022-0396(76)90011-5
10.1201/9780203744376-32
10.1002/mma.3149
10.1088/0951-7715/29/8/2417
10.1016/0022-0396(88)90147-7
10.1016/j.nonrwa.2011.07.006
10.1007/PL00009907
10.1142/S0218202517500282
10.1007/s11538-013-9838-1
10.1002/mma.1346
10.1016/0022-5193(71)90050-6
10.4153/CJM-2000-024-x
10.1007/s00030-017-0472-8
10.1007/s10440-016-0089-7
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References 22
23
24
25
26
27
Fujie K (7) 2016; 29
Gilbarg D (9) 2015
Nagai T (18) 1998; 8
10
11
12
13
14
15
16
17
19
1
4
5
6
8
Brezis H (3) 1983
Olga Aleksandrovna Ladyzhenskaya V A (20) 1988; 23
Biler P (2) 1999; 9
21
References_xml – ident: 12
  doi: 10.1090/mmono/114
– volume: 9
  start-page: 347
  issn: 1343-4373
  year: 1999
  ident: 2
  publication-title: Adv. Math. Sci. Appl.
– ident: 6
  doi: 10.3934/dcdsb.2016.21.81
– ident: 15
  doi: 10.1002/mma.3489
– year: 2015
  ident: 9
  publication-title: Elliptic Partial Differential Equations of Second Order
– ident: 1
  doi: 10.1080/03605307908820113
– ident: 26
  doi: 10.1016/j.na.2018.01.002
– year: 1983
  ident: 3
– ident: 5
  doi: 10.1103/PhysRevLett.108.198102
– ident: 19
  doi: 10.1002/cpa.3160440705
– ident: 21
  doi: 10.1006/jdeq.1993.1045
– ident: 14
  doi: 10.1016/0022-0396(76)90011-5
– ident: 24
  doi: 10.1201/9780203744376-32
– ident: 8
  doi: 10.1002/mma.3149
– volume: 29
  start-page: 2417
  issn: 0951-7715
  year: 2016
  ident: 7
  publication-title: Nonlinearity
  doi: 10.1088/0951-7715/29/8/2417
– ident: 17
  doi: 10.1016/0022-0396(88)90147-7
– ident: 22
  doi: 10.1016/j.nonrwa.2011.07.006
– ident: 10
  doi: 10.1007/PL00009907
– volume: 8
  start-page: 145
  issn: 1343-4373
  year: 1998
  ident: 18
  publication-title: Adv. Math. Sci. Appl.
– ident: 23
  doi: 10.1142/S0218202517500282
– ident: 4
  doi: 10.1007/s11538-013-9838-1
– ident: 25
  doi: 10.1002/mma.1346
– ident: 13
  doi: 10.1016/0022-5193(71)90050-6
– ident: 11
  doi: 10.4153/CJM-2000-024-x
– ident: 16
  doi: 10.1007/s00030-017-0472-8
– volume: 23
  year: 1988
  ident: 20
  publication-title: Linear and Quasi-Linear Equations of Parabolic Type
– ident: 27
  doi: 10.1007/s10440-016-0089-7
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Snippet This paper deals with a Keller-Segel type parabolic-elliptic system involving nonlinear diffusion and chemotaxis in a smoothly bounded domain , , under no-flux...
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iop
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SubjectTerms chemotaxis
global existence
Lyapunov functional
motility function
Title Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis systems without gradient sensing
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